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A ball is thrown into the air with an upward velocity of 40 ft/s. Its height h in feet after t seconds is given by the function h = −16t2+ 40t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?

Respuesta :

bcalle
The maximum(or minimum) of a parabolic function would be it's vertex.
To find the vertex use the formula x = -b/(2a), after finding x, plug x back into the function to find y.
The function needs to be in standard form ax^2 + bx + c, so
a = -16, b = 40
x = -40/(2*-16) = 1.25
y = -16(1.25)^2 + 40(1.25) + 10
y = -25 + 50 +10
y = 35
The maximum height is the y value of the vertex. 35 feet is the answer.

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